Hey can anyone help me prove this problem?
Let A and B be a subsets of R and bounded above.
Let InfA=a and InfB=b.
Let C= {xy ; x belongs to A, and y belongs to B}
Prove that InfC=ab
This problem isn't true as stated.
1) I think you're intending to assume that A and B are bounded below.
2) Let A = {-1, 1}, B = {-1}. Then a = -1, b = -1, so ab = 1. Also C = {-1, 1}, so inf(C) = -1.
Thus inf(C) is NOT equal to ab.